remote thermometer for a pool

I have created a controller for my pool where i can set a timer to run the pump, turn the heat and light on and off, etc. My next task is to get some sort of wireless thermometer to tell Arduino the water temp so that i can display it on the web page and smart phone.

Originally, i had hoped to get a wireless pool thermometer that transmits an RF signal and try to capture that. From what i have been reading, that is not really feasible. My next thought is the following?

Set up a small arduino with a DS18B20 temperature sensor and an rf transmitter. I can then install the rf receiver on my controller board to receive all of this data. I can put the transmitting arduino in a small watertight case with the rf transmitter and run the wire for the sensor through a small hole in the box and then seal it up well. I already fired out how to mount it. This would also have to run on battery power.

Anyone have any suggestions?

Originally, i had hoped to get a wireless pool thermometer that transmits an RF signal and try to capture that. From what i have been reading, that is not really feasible.

What's the issue with this approach?

Im wondering if anyone has any ideas on this for instance:

What arduino to use? What is the physically smallest arduino i can use?
im assuming i can just use a 9v transistor battery and connect it directly to the board by soldering the 9v battery connector wire. is that correct?
What sort of battery life can i expect from this? Im thinking to set it the code with a 1 minute delay so that it is not constantly transmitting a signal and thus killing the battery.

9V batteries do not hold long (depends on your HW schema), LIPO have often a much higher mAH rating.

to save battery read this - Gammon Forum : Electronics : Microprocessors : Power saving techniques for microprocessors -
Maybe think of a small solar panel and a rechargeable battery

I gave just gotten an ATtiny85 working with some 433Mhz Tx/Rx.

A temperature sensor would be easy to add on...
The ATtiny85 use extremely little power.

With the 10ma TX which will be the largest overhead only being used for maybe 1 second maximum (use a transistor to switch it on only when about to send data)...a 9v battery at 200mAh could give you weeks of power.